Lab 14 Objectives

In this lab, we will use S-Plus to carry out logistic regressions using the Low Birth Weight data. Read in the data lowbwt for the last time! (since you have used it before, restore your previous dataset)

Follow Along Exercise 7 in Chapter 20...

Because we want to model a dichotomous variable, grmhem, germinal matrix hemorrhage, we cannot use linear regression methods. Logistic regression models the log odds as a linear function of the explanatory variables. In this case we start by assuming that the log odds of a hemorrhage depend on the infants 5 minute apgar score, apgar5.

To fit this model, go to the Statistics and select Regression, then scroll down to Logistic. In the dialog box enter grmhem as the dependent variable in the model formula and the select apgar5 for the independent variable. The model formula should look like grmhem ~ apgar5, which is the same form as we used in simple linear regression, however here we are using a logit link function to show how the mean relates to the explanatory variables. (it also makes the probabilities stay between 0 and 1). Click OK. the output will appear in the report window.

(a) From the output interpret the estimate of the coefficient of apgar5. (remember the units of apgar5)

(b) From the equation for the estimated log odds, calculate the log odds for an apgar5 score of 3. Transform back from log odds to odds, then from odds to the probability. Repeat for apgar5 = 7.

(c) Using your output, construct a Z-score for testing that the coefficient for apgar5 is zero. What is the p-value?

(d) Now fit the logistic model using tox (tox = 1 for toxemia, tox=0, no toxemia). How should the coefficients be interpreted?

(e) From your output what are the odds of a hemorrhage for mothers with toxemia? What is the probability of hemorrhage for mothers with toxemia? Repeat for mothers without toxemia.

(f) What is the odds ratio of hemorrhage for children whose mothers had toxemia relative to those whose mothers were not diagnosed with toxemia? Calculate from the predicted probabilities from (e) and also directly from the estimated coefficient for tox.

(g) Using the estimates and standard errors from the output, construct a 95% confidence interval for the population odds ratio in (f). Use [exp(b -1.96 se(b)), exp(b+1.96 se(b))] where b is the estimated coefficient.